Aluminum definitely causes Aluminum Intoxication. This was clearly demonstrated in patients with reduced renal function in the late 1980s.
Before that, technical limits on measuring Al couldnt detect the small but significant absorption of Al, so on a large scale, what you could measure in intake, pretty much was the same that came out -
That's why, before the late 1980s, Aluminum salts, not known for their solubility, were declared non-absorbable.

Now a variety of studies have clarified that aluminum does get absorbed in small quantities from the gut and the lungs. Some of this aluminum is bound into bone, and, if the kidneys are working adequately, aluminum doesnt reach toxic levels for the most sensitive tissues: brain; bone; and blood forming cells (inside bone).

The details of aluminum intoxication remain obscure, since aluminum is common in the environment,
and its toxicity is chronic rather than acute.
The symptoms of aluminum intoxication include disorganized behavior - consistent with dementia, as well as toxic effects on bone and blood (see review article).

Since renal function declines with aging, and brain and bone problems commonly afflict the elderly, we can prudently minimize aluminum intake from food and drugs in the elderly -
and you're probably never too young to start.
Aluminum plays no known useful role in the body, so we don't need aluminum to be healthy. We know that too much aluminum is harmful. While the details are being studied, we can all easily minimize our Aluminum intake, by just avoiding alum and other aluminum salts in our food and drugs.

The question of aluminum and Alzheimers disease cant be answered simply because of the vague definition of what we now call Alzheimers Disease.

For the indefinite future, it's likely that aluminum intoxication, Alzheimers disease and other forms of dementia will be confused with each other. Minimizing the intake of aluminum, which we know can cause brain disease, is a simple, feasible and practical response to our concerns about dementia and aging.